Method of moments in analysis of x-ray diffraction lines

A general relation between the moments of the functionsf,g, andh, in the integral equationh(x)=f(y)g(x–y) dy, is derived. This enables any moment of the unknown functionf to be calculated from the moments of the functionsg andh. In particular, if certain assumptions are fulfilled, the moments of the components of the doublet can be calculated with advantage from the moments of the total profile. The statistical significance of the moment characteristics is also emphasized.

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f, g, h h(x)=f(y)g(x–) dy, f g h. , . .

     

Single crystal diffraction patterns of germanium. Part II

The rocking curves of Ge (111), (220), (333) for CuK ₁ radiation were measured by means of the triple-crystal diffractometer. Perfect silicon single crystals, cut parallel to the (111) plane were used in the monochromator part of the triple-crystal diffractometer. The results prove the suitability of such a monochromator for studying diffraction patterns.

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. II

(rocking curves) (111), (220), (333) CuK ₁ . , (111). .

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In conclusion the authors thank A. Haruý for preparing the germanium single crystals and they are indebted to V. Smutná and A. Irra for the care with which they carried out various tasks.     

Double crystal spectrometer with relatively high vertical divergence and instrumental distortion of X-ray spectra

The problem of vertical divergence on the double-crystal spectrometer is treated, both theoretically and experimentally. It is shown that, even in the case of finite vertical divergence, one may get the resulting profile of the measured spectral line as a convolution of the true spectral line and the instrumental smearing function. The general method of calculating this smearing function is given. Further, the influence of the vertical divergence is separated, and some general features are derived.In the experimental part, a double-crystal spectrometer for the fluorescent method of excitation and the precise adjustment of the instrument is described in detail.The theoretical formulas concerning instrumental smearing, the dependence of the peak intensity and the shift of the maximum on the vertical divergence are verified experimentally.     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

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, . , . , , . , . .

     

Содержания работ, выш едших толъко в чешско м издании настояшего ж урнала (Československý časopis pro fysiku)

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Abstracts of papers which have appeared only in the czech edition of this journal (eskoslovenský asopis pro fysiku)

     

Single crystal diffraction pattern of germanium

The diffraction pattern for the (111)-reflection of germanium was measured by means of the three-crystal arrangement and compared with dynamical theory. The results obtained indicate the possibility of using germanium crystals for precise measurements in X-ray spectroscopy.

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(111) . .

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In conclusion the authors thank Ing. Hrubý for preparing the germanium single crystals and participating in the preparation of the surfaces; they are also indebted to V. Smutná, R. ída and A. Irra for the care with which they carried out various tasks and V. Horáková for carefully performing the numerical calculations.     

The single crystal diffraction patterns of silicon

A triple-crystal diffractometer is used to study the single crystal diffraction patterns of Si (111), (220), (333) and good agreement with the dynamical theory of X-ray diffraction on perfect single crystals is found. This proves the possibility of using Si single crystals as in X-ray spectroscopy for a double-crystal spectrometer with a high resolving power as well as for studying very narrow diffraction patterns by means of a triple-crystal diffractometer.

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Si

Si (111), (220), (333); . Si , .

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The authors thank R. ida and F. Hájek for designing and making the automatic equipment for measuring the curves and V. Smutná and A. Irra for carefully performing the auxiliary work.     

On practical calculations with reflection curves for perfect crystals

The application of the Prins function for practical calculations is rather laborious. In the present article it is shown by analysis of some of the properties of this function that in most experiments with perfect crystals one may use functions of a much simpler form. Such a function is proposed, its use is shown on some examples, a method of simplified calculation of the fundamental constants of the Prins function is given, and finally some numerical examples are added as illustration.

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. , . , , , , .

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These curves will be hereafter called Prins functions.

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The author is greatly indebted to M. Malkovská for the experimental data in Chapter VI. C and to V. Horáková for numerical computations of the integrals in Appendix 2.     

The space group symmetry of surface structure

The symmetry of a crystal with an ideal surface is investigated. It is shown that the two-dimensional space group symmetry of the crystal should be used rather than the pure translational symmetry.